Multi-agent systems often involve multi-level interactions that make strategic reasoning hard to scale. To capture such systems, we introduce hierarchical concurrent game models (HCGMs) that allow embedding of (sub)systems into other systems. We define the semantics of ATL on HCGMs by an unfolding of an HCGM into a standard (flat) concurrent game model. Building on this semantics, we provide a model checking algorithm for ATL interpreted over HCGMs and discuss its complexity.

We present NatSTV, a tool for approximate verification of natural strategic ability in multi-agent systems. The tool builds on our model checker STV (STrategic Verifier), and implements heuristic synthesis of natural strategies for asynchronous agents with imperfect information and recall. All of that is available through a web interface, with no need to install or configure the software by the user.

Verification of strategic ability under imperfect information is challenging, with complexity ranging from NP-complete to undecidable. This is partly because traditional fixpoint equivalences fail in this setting. Some years ago, an interesting idea of fixpoint approximation was proposed for model checking of ATL_ir, i.e., the logic of strategic ability for agents with imperfect information and imperfect recall. In this paper, we propose a new variant of the approximation, that uses the agent's local model rather than the global model of the system. We prove correctness of the construction, and demonstrate its effectiveness through experimental results on scalable models of voting.

In this paper, we present a substantially enhanced version of our software tool STV (STrategic Verifier), dedicated to strategy synthesis and model checking of strategic abilities in multi-agent systems. The new extension, called STV+FLY, incorporates an advanced strategy synthesis algorithm that enables model checking with on-the-fly generation of the global model. This innovative approach allows for the verification of some strategic properties without generating the entire global state space, thus avoiding an important bottleneck and significantly improving the efficiency.

Formal analysis of security is often focused on the technological side of the system. One implicitly assumes that the users will behave in the right way to preserve the relevant security properties. In real life, this cannot be taken for granted. In particular, security mechanisms that are difficult and costly to use are often ignored by the users, and do not really defend the system against possible attacks. Here, we propose a graded notion of security based on the complexity of the user’s strategic behavior. More precisely, we suggest that the level to which a security property φ is satisfied can be defined in terms of: (a) the complexity of the strategy that the user needs to execute to make φ true, and (b) the resources that the user must employ on the way. The simpler and cheaper to obtain φ, the higher the degree of security. We demonstrate how the idea works in a case study based on an electronic voting scenario. To this end, we model the vVote implementation of the Prêt à Voter voting protocol for coercion-resistant and voter-verifiable elections. Then, we identify “natural” strategies for the voter to obtain voter-verifiability, and measure the voter’s effort that they require. We also consider the dual view of graded security, measured by the complexity of the attacker’s strategy to compromise the relevant properties of the election.

Some multi-agent scenarios call for the possibility of evaluating specifications in a richer domain of truth values. Examples include runtime monitoring of a temporal property over a growing prefix of an infinite path, inconsistency analysis in distributed databases, and verification methods that use incomplete anytime algorithms, such as bounded model checking. In this paper, we present multi-valued alternating-time temporal logic ( mv-ATL → ∗ ), an expressive logic to specify strategic abilities in multi-agent systems. It is well known that, for branchingtime logics, a general method for model-independent translation from multi-valued to two-valued model checking exists. We show that the method cannot be directly extended to mv-ATL → ∗ . We also propose two ways of overcoming the problem. Firstly, we identify constraints on formulas for which the model-independent translation can be suitably adapted. Secondly, we present a model-dependent reduction that can be applied to all formulas of mv-ATL → ∗ . We show that, in all cases, the complexity of verification increases only linearly when new truth values are added to the evaluation domain. We also consider several examples that show possible applications of mv-ATL → ∗ and motivate its use for model checking multi-agent systems.

In this paper we introduce Strategy Logic with simple goals (SL[SG]), a fragment of Strategy Logic that strictly extends the well-known Alternating-time Temporal Logic ATL by introducing arbitrary quantification over the agents' strategies. Our motivation comes from game-theoretic applications, such as expressing Stackelberg equilibria in games, coercion in voting protocols, as well as module checking for simple goals. Most importantly, we prove that the model checking problem for SL[SG] is PTIME-complete, the same as ATL. Thus, the extra expressive power comes at no computational cost as far as verification is concerned.